I am asking this question so that I want to easily know how many transactions occurred at a particular Bitcoin price. For example, at the price of $20T per BTC, how many are they?
There could be other ways finding this correlation, but my question is: Does the block stores this dollar value?
It does not.
Each block contains a list of transactions and other metadata such as block number, timestamp when it was mined, etc... But the fiat monetary value is not part of the block, nor a part of a transaction.
You'll also need to define a source of truth for the price. While a specific block was mined on a specific time, the price of Bitcoin at that specific time was slightly different on each exchange.
Example (values are made up):
Block number 500,000 was mined on 2022-01-01 00:00:00.
At this exact time, the highest bid on Binance was $19,990, the lowest ask on Binance was $20,000, the highest bid on Coinbase was $20,050, the lowest ask on Coinbase was $20,070, etc.
Exchanges and aggregation services (such as Coinmarketcap) often offer some average prices through their API for a specified timeframe. But there's no "one price of Bitcoin at a specified time".